The minimum length of the intercept between the coordinate axes made by a tangent of the ellipse $\frac{x^2}{64}+\frac{y^2}{4}=1$ is

If the straight line $x \cos \alpha + y \sin \alpha = p$ touches the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$,then prove that $a^{2} \cos^{2} \alpha + b^{2} \sin^{2} \alpha = p^{2}$.

The eccentricity of the ellipse $4x^2 + 9y^2 + 8x + 36y + 4 = 0$ is

Let the common tangents to the curves $4(x^{2}+y^{2}) = 9$ and $y^{2} = 4x$ intersect at the point $Q$. Let an ellipse,centered at the origin $O$,have lengths of semi-minor and semi-major axes equal to $OQ$ and $6$,respectively. If $e$ and $l$ respectively denote the eccentricity and the length of the latus rectum of this ellipse,then $\frac{l}{e^{2}}$ is equal to

The length of the latus rectum of the ellipse $9x^2 + 4y^2 = 1$ is

Find the coordinates of the foci,the vertices,the lengths of the major and minor axes,and the eccentricity of the ellipse $9x^{2} + 4y^{2} = 36$.